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On a problem of A. N. Kolmogorov for functions of two variables

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Literature cited

  1. A. N. Kolmogorov, “Zur Grossenordnung des Restgliedes fourierscher Reiher differenzierbarer Funktionen,” Annals of Math.,36, No. 2 (1935).

  2. S. M. Nikol'skii, “Asymptotic behavior of the remainder for approximation of functions satisfying a Lipschitz condition, using Fejer summation,” Izv. Akad. Nauk SSSR, Ser. Matem., No. 4 (1940).

  3. S. M. Nikol'skii, “Methods of approximation by trigonometric sums,” Izv. Akad. Nauk SSSR, Ser. Matem., No. 4 (1940).

  4. S. M. Nikol'skii, “Asymptotic estimates of the remainder for approximation by Fourier sums,” Dokl. Akad. Nauk SSSR,32, No. 6 (1941).

  5. S. M. Nikol'skii, “Approximation of periodic functions by trigonometric polynomials,” Trudy Mat. Inst. im. V. A. Steklova, AN SSSR,15 (1945).

  6. N. P. Korneichuk, “On the approximation of periodic functions satisfying a Lipschitz condition, by Bernstein-Rogosinskii sums,” Dokl. Akad. Nauk SSSR,125, No. 2 (1959).

  7. N. P. Korneichuk, “Estimates for the approximation of the class Hα by trigonometric polynomials,” in; Contemporary Problems in the Constructive Theory of Functions [in Russian], Fizmatgiz (1961).

  8. A. V. Efimov, “Approximation of some classes of continuous functions by Fourier and Fejer sums,” Izv. Akad. Nauk SSSR, Ser. Matem., No. 23 (1958).

  9. A. V. Efimov, “Approximation of functions with a given modulus of continuity by Fourier sums,” Izv. Akad. Nauk SSSR, Ser. Matem.,23, No. 1 (1959).

  10. A. V. Efimov, “On the approximation of periodic functions by de la Vallée-Poussin sums,” Izv. Akad. Nauk SSSR, Ser. Matem.,23, No. 5 (1959).

  11. A. V. Efimov, “Approximation of continuous periodic functions by Fourier sums,” Izv. Akad. Nauk SSSR, Ser. Matem.,24, No. 2 (1960).

  12. A. V. Efimov, “Linear methods of approximation for certain classes of continuous periodic functions,” Trudy Mat. Inst. im. V. A. Steklova, AN SSSR,62 (1961).

  13. S. A. Telyakovskii, “Approximation of differentiable functions by linear means of their Fourier series,” Izv. Akad. Nauk SSSR, Ser. Matem.,24, No. 2 (1960).

  14. S. A. Telyakovskii, “The norm of trigonometric polynomials and approximation of differentiable functions by linear means of their Fourier series. I,” Trudy Mat. Inst. im. V. A. Steklova, AN SSSR,62 (1961).

  15. S. A. Telyakovskii, “The norm of trigonometric polynomials and approximation of differentiable functions by linear means of their Fourier series. II,” Izv. Akad. Nauk SSSR, Ser. Matem.,27, No. 2 (1963).

  16. S. A. Telyakovskii, “Conditions for the integrability of trigonometric series and their application to the study of linear methods of summation of Fourier series,” Izv. Akad. Nauk SSSR, Ser. Matem.,28, No. 6 (1964).

  17. P. T. Bugaets, “Asymptotic estimates of the error for approximation of functions of two variables by Fourier sums,” Dokl. Akad. Nauk SSSR,79, No. 4 (1951).

  18. I. P. Natanson, Theory of Functions of alfeal Variable [in Russian], Gostekhizdat (1957).

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Authors and Affiliations

  1. Academy of Sciences of the Ukrainian SSR, Ukraine

    A. I. Stepanets

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  1. A. I. Stepanets
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 24, No. 5, pp. 653–665, September–October, 1972.

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Stepanets, A.I. On a problem of A. N. Kolmogorov for functions of two variables. Ukr Math J 24, 526–536 (1972). https://doi.org/10.1007/BF01090536

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  • DOI: https://doi.org/10.1007/BF01090536

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